Measurement and ComparisonDate: 04/30/99 at 09:43:41 From: Joanne Tranter Subject: Measurement Why is comparison the key to measurement? Date: 04/30/99 at 18:11:19 From: Doctor Rick Subject: Re: Measurement Hi, Joanne. I don't know the context of your question - why you are asking it - so I don't know what kind of answer you need. But I agree with the statement. It's easiest to see when you measure length. You measure the width of a sheet of paper, for instance, by putting a ruler next to it and COMPARING the width with the positions of the markings on the ruler. You determine that it is between the 8 1/2 and 8 9/16 inch markings, perhaps. This means that the length is greater than 8 1/2 and less than 8 9/16 inches - those are comparisons. Where did the ruler come from? When it was manufactured, it (or the machine that made it, at least) was calibrated against a standard ruler. That standard can trace its lineage to a metal bar of a certain composition, kept in certain conditions, in Washington or London or Paris. Such a standard bar was once the official definition of the foot, or whatever. Now the inch is defined as exactly 2.54 cm, and the meter is defined in terms of a certain number of wavelengths of light produced by a certain kind of atom under certain conditions. The "certain conditions" in both the old and new standards reflect the need to have a standard, against which to compare our measuring instruments, that does not change over time. The particular atom was chosen for this reason. Here is a reference on the history of the length standard, from the US National Institute of Standards and Technology (NIST): http://physics.nist.gov/cuu/Units/meter.html The same story can be told about weights. A typical bathroom scale measures your weight by the compression of a spring; it is calibrated by checking how much the spring is compressed by certain known weights, so that measurement with the scale consists of comparing the compression caused by your body with the compression caused by these known weights. But where precision is needed, a spring scale is not used. Instead, a balance is used - a simple two-pan balance, or a triple-beam balance. In either case, the object to be weighed is actually compared against a standard weight that is right there on the scale. (With a triple- beam balance, just a few weights can be compared with any test weight by using a lever principle; the lengths of the lever arms must have been calibrated by comparison with a standard when the balance was made.) We have had questions about whether a balance measures mass or weight (the force of gravity on an object). The answer is that, though it depends on gravity and compares the force of gravity on the test mass and the standard mass, it is comparing against a standard MASS. If the balance were taken to the moon, the forces of gravity on the two masses would be different, but the COMPARISON would be exactly the same because the forces are reduced by exactly the same amount. In contrast, the bathroom scale would indicate that you weigh a lot less, because it is actually comparing the FORCE of gravity against the force exerted by the spring. It would need to be seriously recalibrated on the moon! If this isn't the kind of answer you are looking for, ask again. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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